These instructions are specific to the US Cellular Samsung Galaxy S4 (SCH-R970).
Although similar methods may work with other phones this method uses methods that may NOT be compatible with any other phone.
If you do not have the US Cellular Samsung Galaxy S4 please DO NOT follow these instructions as they will most likely brick your phone!

Prerequisites

A PC running Windows with the Samsung Mobile Drivers Installed. The Samsung Mobile Drivers are available here.

The stand-alone version of Odin (I use v1.85). Various versions of Odin are available here.

The Recovery version of your choice in a TAR format. Official CWM at www.clockworkmod.com and is Garwynn's personal recommendation.

Superuser (or SuperSU, MIUI Security, and etc) in a flashable zip. For this method I used SuperSU 1.25 (but any SU in a flashable ZIP should work). You can download several different versions here.

Although not required it is recommended that you have Samsung Kies installed (but not running) on your PC as well. You can download Samsung Kies here.

Open Odin. When it is opened you will be presented with a window that has a black title bar across the top, several empty boxes and a few other buttons.Please be very careful here not to select anything unless specifically told to do so. Improper use of Odin CAN and WILL brick your device.

Select the PDA option in Odin.

Navigate to where you saved the custom recovery TAR on your PC and select it.

Reboot your phone into Download/Odin Mode by holding down the Power and Volume Down buttons.When rebooting to Download/Odin Mode timing is critical. When you see the Samsung logo appear on your screen release the three keys. If your timing is off by just a little bit your phone will boot normally.

When prompted press the Volume Up key to continue.

Plug your USB cord into your phone and then plug the other end of the cord into an available USB slot.

Once the phone is plugged in you should see one of the white boxes in Odin turn yellow and display a random COM number.

Press Start in Odin.
If the flash is successful your phone will now reboot. This will take slightly longer than usual, this is normal. Please be patient while your phone reboots.